Fundamentals Of Thermal-fluid Sciences In Si Units
5th Edition
ISBN: 9789814720953
Author: Yunus Cengel, Robert Turner, John Cimbala
Publisher: McGraw-Hill Education
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Chapter 12, Problem 57P
To determine
The initial discharge velocity.
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2. Consider a polymeric membrane within a 6 cm diameter stirred ultrafiltration cell. The membrane is
30 μm thick. The membrane has pores equivalent in size to a spherical molecule with a molecular weight
of 100,000, a porosity of 80%, and a tortuosity of 2.5. On the feed side of the membrane, we have a
solution containing a protein at a concentration of 8 g L-1 with these properties: a = 3 nm and DAB = 6.0 ×
10-7 cm² s¹. The solution viscosity is 1 cP. The hydrodynamic pressure on the protein side of the
membrane is 20 pounds per square inch (psi) higher than on the filtrate side of the membrane. Assume
that the hydrodynamic pressure difference is much larger than the osmotic pressure difference
(advection >> diffusion). Determine the convective flow rate of the solution across the membrane.
1. Calculate the filtration flow rate (cm³ s¹) of a pure fluid across a 100 cm² membrane. Assume the
viscosity (µ) of the fluid is 1.8 cP. The porosity of the membrane is 40% and the thickness of the
membrane is 500 μm. The pores run straight through the membrane and these pores have a radius of
0.225 μm. The pressure drop applied across the membrane is 75 psi. (Note: 1 cP = 0.001 N s m²² = 0.001
Pa s.)
3. Tong and Anderson (1996) obtained for BSA the following data in a polyacrylamide gel for the
partition coefficient (K) as a function of the gel volume fraction (4). The BSA they used had a molecular
weight of 67,000, a molecular radius of 3.6 nm, and a diffusivity of 6 × 10-7 cm2 s-1. Compare the
Ogston equation
K=exp
+
to their data and obtain an estimate for the radius of the cylindrical fibers (af) that comprise the gel.
Hint: You will need to plot Ink as a function of gel volume fraction as part of your analysis. Please include
your MATLAB, or other, code with your solution.
Gel Volume Fraction (4)
KBSA
0.00
1.0
0.025
0.35
0.05
0.09
0.06
0.05
0.075
0.017
0.085
0.02
0.105
0.03
Chapter 12 Solutions
Fundamentals Of Thermal-fluid Sciences In Si Units
Ch. 12 - Prob. 1PCh. 12 - Express the Bernoulli equation in three different...Ch. 12 - What are the three major assumptions used in the...Ch. 12 - Define static, dynamic, and hydrostatic pressure....Ch. 12 - Prob. 5PCh. 12 - Prob. 6PCh. 12 - Prob. 7PCh. 12 - How is the location of the hydraulic grade line...Ch. 12 - Prob. 9PCh. 12 - Prob. 10P
Ch. 12 - A glass manometer with oil as the working fluid is...Ch. 12 - The velocity of a fluid flowing in a pipe is to be...Ch. 12 - The water level of a tank on a building roof is 20...Ch. 12 - Prob. 14PCh. 12 - Prob. 15PCh. 12 - Prob. 16PCh. 12 - Prob. 17PCh. 12 - Prob. 18PCh. 12 - A piezometer and a Pitot tube are tapped into a...Ch. 12 - The diameter of a cylindrical water tank is Do and...Ch. 12 - Prob. 21PCh. 12 - Prob. 22PCh. 12 - Prob. 23PCh. 12 - An airplane is flying at an altitude of 12,000 m....Ch. 12 - While traveling on a dirt road, the bottom of a...Ch. 12 - Prob. 26PCh. 12 - Prob. 27PCh. 12 - Air at 105 kPa and 37°C flows upward through a...Ch. 12 - A handheld bicycle pump can be used as an atomizer...Ch. 12 - Prob. 31PCh. 12 - The water pressure in the mains of a city at a...Ch. 12 - Prob. 33PCh. 12 - Air is flowing through a venturi meter whose...Ch. 12 - The water level in a tank is 15 m above the...Ch. 12 - What is useful pump head? How is it related to the...Ch. 12 - Prob. 38PCh. 12 - What is irreversible head loss? How is it related...Ch. 12 - Consider the steady adiabatic flow of an...Ch. 12 - Prob. 41PCh. 12 - Prob. 42PCh. 12 - Prob. 43PCh. 12 - Prob. 44PCh. 12 - In a hydroelectric power plant, water flows from...Ch. 12 - Reconsider Prob. 12–45E. Determine the flow rate...Ch. 12 - Prob. 47PCh. 12 - Water is being pumped from a large lake to a...Ch. 12 - A 15-hp (shaft) pump is used to raise water to a...Ch. 12 - Prob. 51PCh. 12 - The water level in a tank is 20 m above the...Ch. 12 - Prob. 53PCh. 12 - Prob. 54PCh. 12 - Water flows at a rate of 20 L/s through a...Ch. 12 - Prob. 56PCh. 12 - Prob. 57PCh. 12 - Prob. 58PCh. 12 - Prob. 59PCh. 12 - Prob. 60PCh. 12 - Prob. 61PCh. 12 - Prob. 62PCh. 12 - Prob. 63PCh. 12 - A 73-percent efficient 12-hp pump is pumping water...Ch. 12 - Prob. 65PCh. 12 - Air flows through a pipe at a rate of 120 L/s. The...Ch. 12 - Air at 100 kPa and 25°C flows in a horizontal duct...Ch. 12 - Prob. 68RQCh. 12 - Prob. 69RQCh. 12 - Prob. 70RQCh. 12 - A 3-m-high large tank is initially filled with...Ch. 12 - Prob. 73RQCh. 12 - Prob. 74RQ
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